where \(R\)  is the reward for cooperating, \(S\)  is the sucker's payoff, \(T\)  is the payoff associated with the temptation to cheat and \(P\)  is the punishment for cheating. In the classical formulation of the game, \(T > R > P > S\)  so that mutual defection is the Nash equilibrium associated with the game. In the context of evolutionary game theory, the model associated with the above symmetric two-player game via replicator dynamics can be written as [1]}
\(\dot{x} = x (1 - x) (r_1(x) - r_2(x)),\) 
